Noise estimation is required in many algorithms to process image or video optimally. For example, in TV system, noise reduction is often applied as the first step to obtain noise-free video sequences. An optimal algorithm of noise reduction first estimates the noise variance of input video sequences, and then performs noise reduction. Noise estimation is very important in this case, because overestimation leads to image blurring and underestimation leads to insufficient noise reduction.
In order to describe the problem of noise estimation, let gt denote the incoming video frame at time instant t and gt(i,j) denote the corresponding pixel value at the coordinates (i,j) where i represents the ordinate and j represents the abscissa. Generally, we assume the input video sequence is corrupted by independent, identically distributed additive and stationary zero-mean Gaussian noise with variance σ02, that is, any pixel gt(i,j) can be denoted as:gt(i,j)=ft(i,j)+nt(i,j),  (1)
where ft(i,j) denotes the true pixel value without noise corruption and nt(i,j) is the Gaussian distributed noise component satisfyingnt(i,j)˜N(0,σ02).  (2)
Thus, the problem of noise estimation is to estimate the noise variance σ02 of the contaminated image gt without the priori information of the original image ft.
A straightforward method of noise estimation is to compute the expectation of the local variance of image gt. This method suffers from the image structure, causing overestimation. To overcome this problem, several methods have been proposed. One method excludes the local variance if the gradient magnitude of the corresponding pixel is greater than a preset threshold. However, the gradient magnitude is also related with the noise variance, so it is difficult to find an appropriate threshold. Other conventional methods first extract the noise component with little structure by applying high-pass filters on the contaminated image gt, and then perform noise estimation on the noise component. One example decomposes the image into a pyramid structure of different block sizes, wherein the noise variance is estimated from a sequence of four smallest block-based local variances at each level. Another example, a Rayleigh distribution is fitted to the magnitude of the intensity gradient, wherein noise variance is estimated based on the attribute that the Rayleigh probability density function reaches maximum at value σ0. Other methods estimate multiplicative as well as additive noise.
All of the above methods utilize the spatial local statistics to estimate noise variance. The estimation accuracy depends on the separation of the noise component and the real image signal. The robustness degrades greatly if most of image contains complicated structure.